Dynamic Weapon-Target Assignment Via HJI Reachability and Marginal-Return Column Enumeration

This paper proposes an integrated dynamic weapon-target assignment (DWTA) framework that unifies physics-based game evaluation with exact combinatorial optimization. Traditional assignment methods relying on nominal kinematics fail against unpredictable adversarial maneuvers. To address this, a physics-informed neural network (PINN) is trained offline to solve the Hamilton-Jacobi-Isaacs equation, mapping the backward reachable tube (BRT). Acting as a high-fidelity approximation of the physical reachability boundary, the learned surrogate evaluates interception feasibility under worst-case evasions. The imposed BRT constraint induces a phase transition that sharply prunes physically unreachable combinations. Operating on this purified search space, a marginal-return column enumeration algorithm solves the resulting nonlinear integer programming problem. Monte Carlo simulations demonstrate that the PINN surrogate maintains high-precision boundaries under extreme dynamics. In large-scale scenarios where commercial solvers time out, the proposed DWTA algorithm consistently delivers high-quality solutions within milliseconds, providing a robust and physically verified decision baseline for closed-loop air defense systems.